A recurring theme in higher Teichmüller theory is to relate surface group representations into higher rank Lie groups with geometric objects. Taking its cue from classical Teichmüller theory, one is often interested in studying the degeneration of these associated geometric objects when the representation leaves all compact sets in the character variety. The celebrated Thurston compactification of Teichmüller space regards Fuchsian representations as marked hyperbolic metrics, where degenerating families of hyperbolic metrics subconverge to measured laminations.
One key aspect of this compactification is that it is a closed ball upon which the mapping class group acts. In years following, there have been numerous different perspectives of the Thurston compactification, using a variety of methods, topological, geometric, analytic and algebraic (see [1]}, [2]}, [3]}, [4]}, [5]}).
